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GPPPU1-8 SY2026 (Poly, Proofs, Cong, Sim, RightTri, Vol, Prob)

Total questions: 110

Worksheet time: 55hrs 0mins

Name
Class
Date
1.

PRIORITY PRACTICE PROBLEMS (u1: Poly)

[BEGIN U1: Exploring Polynomial Expressions Through Geometry]

These problems are grouped in sets of 4 in this order ... 1. Add / Subtract Polynomials 2. Multiply Polynomials 3. Perimeter of <?> 4. Area of <?>




What is PERIMETER?

4 lines
2.

Simplify this expression:
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)

a)
11a3 - 4a2 - 14a - 7 
b)
5a3 - 4a2 - 14a - 7 
c)
5a3 - 4a2 - 20a - 7 
d)
5a3 - 9a2 - 20a - 7
3.

 Simplify this expression:
(r + 7)(r − 7) 

a)
r 2 − 49 
b)
r 2 + 14
c)
r 2 − 7r + 49 
4.

Find the perimeter of the triangle ...

a)

4x+644x+64

b)

4x2+644x^2+64

c)

3x+503x+50

d)

3x2+503x^2+50

5.

The following image is a square. Find the PERIMETER AND AREA of the square.

a)

PERIMETER: 16x316x^3 AREA: 16x616x^6

b)

PERIMETER: 16x616x^6 AREA: 16x316x^3

c)

PERIMETER: 8x38x^3 AREA: 8x68x^6

d)

PERIMETER: 8x68x^6 AREA: 8x38x^3

6.

Simplify this expression:
(2a2 + 5a + 3) - (a2 - 3a - 4)

a)

3a2 + 2a - 1

b)

a2 + 8a + 7

c)

3a2 + 8a + 7

d)

a2 + 2a - 1

7.

Simplify this expression:
(3x – 1)(x + 5) 

a)
3x2 + 4x + 5
b)
3x2 + 4x - 5
c)
3x2 + 14x + 5
d)
3x2 + 14x - 5
8.

Find the perimeter of the rectangle ...

a)
P= 10x + 2
b)
P= 12x
c)
P = 12
d)
P = 6x2 + 3x
9.

Find the area of the rectangle ...

a)
A= 10x + 2
b)
A= 6x2 + 3x
c)
A= 9x
d)
A= 6x+ 3
10.

Simplify this expression:

(x2 + 5x - 4) - (- x2 + 4x + 6)

a)

2x2 + x + 2

b)

x + 2

c)

2x2 + x - 10

d)

x - 10

11.

Simplify this expression:
(3x2 – 1)(x2 + 5) 

a)

17x2 -5

b)

3x4 + 7x2 - 5

c)

3x4 + 14x2 - 5

d)

3x4 + 14x2 + 5

12.
a)

6b

b)

b + 5

c)

b + 9

d)

b - 13

13.

Find the area of the rectangle ...

a)

42x3+28x242x^3+28x^2

b)

42x2+28x42x^2+28x^{ }

c)

42x3+4x242x^3+4x^2

d)

13x3+11x213x^3+11x^2

14.

Simplify this expression:
(3x2 + 4x – 1)(x2 + 5) 

a)

3x4 + 4x3 + 14x2 + 20x − 5

b)

3x4 + 4x3 + 14x2 + 20x + 5

c)

3x4 + 4x3 - x2 - 5

d)

15x2 + 20x - 5

15.

Simplify this expression:
(4a2 + 5a + 4) - (2a2 - 8a - 4)

a)

6a2 - 3a + 8

b)

2a2 + 13a

c)

2a2 + 13a + 8

d)

6a2 - 3a

16.
a)

4x

b)

4x + 30

c)

4x - 30

d)

4x + 2

17.

Find the area of the rectangle ...

a)

18x2−48x+618x^2-48x+6

b)

18x3−48x+6x18x^3-48x+6x

c)

18x3−48x2+6x18x^3-48x^2+6x

d)

9x3−14x2+7x9x^3-14x^2+7x

18.

Simplify this expression:

(2x2 + 6x - 3) - (- 2x2 - 4x + 6)

a)

4x2 + 10x + 9

b)

10x + 9

c)

10x - 9

d)

4x2 + 10x − 9

19.

Simplify this expression:
(3x2 + 4x – 1)(3x2 + 5) 

a)

9x4 + 12x3 + 12x2 + 20x + 5

b)

3x4 + 4x3 + 14x2 + 20x + 5

c)

3x4 + 4x3 - x2 - 5

d)

9x4 + 12x3 + 12x2 + 20x − 5

20.

What is the perimeter of the rectangle?

a)

24w3 – 4

b)

24w5 – 4

c)

17w2 + 3w3

d)

32w3 + 16w2 – 8

21.

Find the perimeter ...

a)

7x + 5

b)

24x + 4

c)

9x + 5

d)

9x2 + 5

22.

The dimensions of a rectangle are (4y2 – y + 6) feet by (2y2 + 3) feet. What is the perimeter of the rectangle?

a)

12y2 – 2y + 18 feet

b)

6y2 – y + 9 feet

c)

2y2 – 2y + 3 feet

d)

12y2 – y + 9 feet

23.

The perimeter of the triangle is 10x+20.

Find the length of the missing side (marked with '?') ...

a)
6x+10
b)
15x+30
c)
5x+10
d)
5x-10
24.

What is the area of the rectangle?

a)

24w3 – 4

b)

56x6 + 56x5 − 32x3 − 32x2

c)

56x6 + 56x5 − 32x3 + 32x2

d)

32w3 + 16w2 – 8

25.
Find a simplified expression for the area of the shaded region.
a)
2x2 + 2x + 13
b)
10x + 5
c)
10x + 13
d)
2x2 + 13
26.

PRIORITY PRACTICE PROBLEMS (u2: Proofs) (Problems 26 - 110)

U2 (Geometric Foundations and Proofs) ... these "Priority Practice Problems" are organized in the following order ...

Vocabulary and Language (5 problems) (26-30)
Angle and Segment Addition (7 problems) (31-37)

Triangle Sum Theorem | Exterior Angles Theorem (13 problems) (38-50)

Parallel Lines (15 problems) (51-65)

Parallel Line Proofs (20 problems) (66-85)

Quadrilateral Properties (10 problems) (86-95)

(Coordinate) Quadrilateral Proofs (15 problems) (96-110)

[BEGIN VOCABULARY and LANGUAGE] ∠1 and ∠3 can best be described as ...

a)
complementary angles
b)
supplementary angles
c)
vertical angles
d)
adjacent angles
27.

In angle ABC, B is the ...

a)

rays

b)

plane

c)

compass

d)

vertex

28.

In angle ABC, BA and BC are ...

a)

rays

b)

plane

c)

compass

d)

vertex

29.

What does this symbol mean?

a)

less than

b)

greater than

c)

congruent

d)

similar

30.

[END VOCABULARY and LANGUAGE] Name that figure!

a)

Point

b)

Line

c)

Line segment

d)

Ray

31.

[BEGIN Angle and Segment Addition] Find the missing segment length / encontrar la longitud del segmento que falta ...

a)

24

b)

6

c)

9

d)

15

32.

Use the figure to write and solve an equation for x.

a)
5
b)
6
c)
7
d)
8
33.
a)
8
b)
12
c)
-4
d)
-8
34.
B is the midpoint of AC.  Find AB.
a)
2
b)
16
c)
8
d)
4
35.
Find the value of ∠A.
a)
25 degrees
b)
30  degrees
c)
35 degrees
d)
90 degrees
36.

Calculate m∠ABC.

a)

45°

b)

60°

c)

105°

d)

15°

37.

[END Angle and Segment Addition] If m∠ABC = 103° find x.

(a)  

38.

[BEGIN Triangle Sum Theorem] The Triangle Sum Theorem: The sum of the 3 angles in a triangle is ______. 

a)
45°
b)
90°
c)
180°
d)
360°
39.

Find the measure of the indicated angle.

a)

135°135\degree  

b)

55°55\degree  

c)

45°45\degree  

d)

60°60\degree  

40.

Find the measure of the indicated angle.

a)

45°45\degree  

b)

33°33\degree  

c)

123°123\degree  

d)

147°147\degree  

41.

[END Triangle Sum Theorem] Solve for x.

a)
16
b)
11
c)
50
d)
6
42.

[BEGIN Exterior Angle Theorem] Which of the following terms best describes Angle d?

a)
Remote interior angle
b)
Corresponding angle
c)
Exterior angle
d)
Interior angle
43.
Which of the following angles are remote interior angles to angle d?
a)
Angle a and Angle b
b)
Angle b and Angle c
c)
Angle a and Angle c
d)
Angle a and Angle b and Angle c
44.

Which two angles are the remote interior angles to Angle W?

a)

Angle X and Angle Y

b)

Angle X and Angle Z

c)

Angle Y and Angle Z

d)

Angle Z and Angle W

45.
Solve for the missing angle with the question mark. 
a)
A
b)
B
c)
C
d)
D
46.

What is the value of the missing angle?

a)

90

b)

100

c)

20

d)

120

47.

What is the value of x?

a)

105°

b)

144°

c)

69°

d)

111°

48.
a)
A
b)
B
c)
C
d)
D
49.

Find the indicated angle measure. (What is ?)

a)

51°

b)

37°

c)

167°

d)

41°

50.

[END Exterior Angle Theorem] What is the value of x?

a)

38

b)

57

c)

76

d)

85

51.

[BEGIN Parallel Lines and Transversals] What word describes line Z?

a)
Transversal
b)
Corresponding
c)

Consecutive Interiors

52.
What angle corresponds to angle 6?
a)
angle 2
b)
angle 4
c)
angle 7
d)
angle 8
53.
Name the angle relationship.
a)
Alternate Interior
b)
Alternate Exterior
c)
Corresponding
d)
Vertical Angles
54.
Name the angle relationship.
a)

Consecutive Interior

b)
Corresponding
c)
Alternate Interiors
d)

Alternate Exteriors

55.
Name the angle relationship.
a)
Alternate Interior
b)
Alternate Exterior
c)
Corresponding
d)
Vertical Angles
56.
If angle 6 is 25 degrees, how many degrees is angle 7?
a)
25 degrees
b)
50 degrees
c)
90 degrees
d)
155 degrees
57.

If the m∡1 = 118o find m∡5

a)

118o

b)

62o

c)

82o

d)

2o

58.

If the m∡7 = 62o find m∡1

a)

62o

b)

28o

c)

118o

d)

138o

59.

If the m∡3 = 81o find m∡6

a)

180o

b)

990

c)

9o

d)

81o

60.

If the m∡2 = 32o find m∡3

a)

132o

b)

32o

c)

148o

d)

58o

61.

If the m∡5 = 125o find m∡1

a)

125o

b)

35o

c)

55o

d)

100o

62.

If the m∡6 = 71o find m∡3

a)

171o

b)

19o

c)

109o

d)

71o

63.

If the m∡3 = 35o find m∡8

a)

35o

b)

550

c)

135o

d)

145o

64.

If the m∡7 = 60o find m∡2

a)

7o

b)

60o

c)

300

d)

120o

65.

[END Parallel Lines and Transversals] Solve for y.

a)

y=55y=55  

b)

y=35y=35  

c)

y=70y=70  

d)

y=45y=45  

66.

[BEGIN Parallel Lines Proofs] If A=B and B=C, then A=C. What is this property?

a)

Transitive

b)

Reflexive

c)

Symmetric

d)

Substitution

67.
If a = b, then a may be replaced by b in any expression.
a)
Transitive Property         
b)
Reflexive Property             
c)
Symmetric Property 
d)
Substitution Property
68.

Analogy


Transitive is to Congruence, as Substitution is to ???

a)

Equalities

b)

Congruences

c)

Both

d)

None of the above

e)

I don't Know

69.
For any number a, a = a.
a)
Transitive Property         
               
b)
Reflexive Property             
c)
Symmetric Property           
d)
Substitution Property
70.

If you know that angles 1 and 2 are vertical, what else do you know?

a)

Angles 1 and 2 are congruent

b)

Angles 1 and 2 are supplementary

c)

Angles 1 and 2 are right angles

d)

Angles 1 and 2 are corresponding angles

71.

If A=10, then wherever there is an "A" value, you could replace it with 10. What property is this?

a)

Substituion

b)

Transitive

c)

Symmetric

d)

Plug it in

72.

When two parallel lines are cut by a transversal, all pairs of angles created are either _________ or _________.

a)

Congruent, supplementary

b)

Congruent, complementary

c)

Supplementary, complementary

d)

Corresponding, vertical

73.

What is the relationship of ∠1 and ∠5?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Vertical Angles

74.

What is the relationship of ∠4 and ∠7?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Linear Pair

75.

What is the relationship of ∠3 and ∠4?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Linear Pair

76.

What is the relationship of ∠6 and ∠8?

a)

Corresponding Angles

b)

Alternate Interior Angles

c)

Alternate Exterior Angles

d)

Consecutive Interior Angles

e)

Linear Pair

77.

What statement can be made from the diagram using the Corresponding Angles Postulate?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

78.

What statement can be made from the diagram using the Alternate Interior Angles Theorem?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

79.

What statement can be made from the diagram using the Alternate Exterior Angles Theorem?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

80.

What statement can be made from the diagram using the Consecutive Interior Angles Theorem?

a)

∠1 and ∠2 are supplementary

b)

m∠1 + m∠2 = 180°

c)

∠1 ≅ ∠2

d)

m∠1 = m∠2

81.

Supply the first statement.

a)

m ll n

b)

< 4 = < 6

c)

Given

d)

Definition of parallel lines

82.

Supply the second reason.

a)

Linear Pair Postulate

b)

Alternate Interior Angles Theorem

c)

Vertical Angles Theorem

d)

Corresponding Angles Postulate

83.

Supply the third reason.

a)

Vertical Angle Theorem

b)

Corresponding Angles Postulate

c)

Alternate Interior Angles Postulate

d)

Same Side Interior Angles Theorem

84.

The last statement is <4 = <6. What is the last reason

a)

Prove

b)

Definition of congruent angles

c)

Transitive Property

d)

Alternate Interior Angles Theorem

85.

[END Parallel Lines Proofs] Which proof is incorrect?

a)

b)

c)

d)

86.

[BEGIN Quadrilateral Properties] What is the most specific name for this shape?

a)

Square

b)

Rectangle

c)

Rhombus

d)

Parallelogram

87.
What shape is this?
a)
Kite
b)
Square
c)
Trapezoid
d)
Rhombus
88.
What shape is this?
a)
Square
b)
Parallelogram
c)
Trapezoid
d)
Rhombus
89.

This is a parallelogram. What is the value of x?

a)

7

b)

12

c)

112

d)

68

90.

This is a parallelogram. What is the value of y?

a)

7

b)

12

c)

112

d)

68

91.

This is a parallelogram. What is the value of a?

a)

7

b)

12

c)

112

d)

68

92.

Select the most specific name for each of the following quadrilaterals shown to the left

a)

Parallelogram

b)

Rhombus

c)

Trapezoid

d)

Square

e)

Rectangle

93.

Select the most specific name for each of the following quadrilaterals shown to the left

a)

Parallelogram

b)

Rhombus

c)

Trapezoid

d)

Square

e)

Rectangle

94.

Find the missing angle.

a)

30

b)

60

c)

90

d)

120

95.

[END Quadrilateral Properties] Find the measure of the angle x.

a)

105

b)

115

c)

65

d)

75

96.

[BEGIN (Coordinate) Quadrilateral Proofs] What is this formula used for?

y2−y1x2−x1\frac{y_2-y_1}{x_2-x_1}  

a)

To find the distance between two points

b)

To find the slope between two points

c)

To find the midpoint between two points

97.

What is the formula below used for?

(x2−x1)2+(y2−y1)2\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}  

a)

To find the distance between two points

b)

To find the slope between two points

c)

To find the midpoint between two points

98.

Josie found the slope of AB to be

34\frac{3}{4} . Use rise over run to check her answer. 

a)

No, the slope should be  43\frac{4}{3}  

b)

She was correct. 

99.

Brad proved that ABCD is a parallelogram by proving both sets of opposite sides to be parallel. What should he do next if he wants to prove it is a rhombus?  

a)

Find the distance of each line to see if they are congruent. 

b)

Compare the slopes of adjacent sides to see if they are perpendicular. 

100.

Brad proved that ABCD is a parallelogram and that all sides had the same distance What should he do next if he wants to prove it is a square?  

a)

He doesn't need to do anything else, it looks like a square so he is all set. 

b)

Compare the slopes of adjacent sides to see if they are perpendicular. 

101.

In the image, side AB has a slope of -3 and AD has a slope of 1/3. What does this mean is true?

a)

Side AB and AD are parallel

b)

Side AB and AD form a right angle

c)

Side AB and AD are congruent

d)

Nothing Specific

102.

Drew used the distance formula and found each side to have a distance of 4. What does that mean?

a)

Side AB and AD are parallel

b)

Side AB and AD form a right angle

c)

Side AB and AD are congruent

d)

Nothing Specific

103.

The slope of side AB is -3 and the slope of DC is -3. What does this mean?

a)

Side AB and AD are parallel

b)

Side AB and AD form a right angle

c)

Side AB and AD are congruent

d)

Nothing Specific

104.

Julia proved ABCD is a parallelogram. She notices that side AB has a slope of 8/3 and BC has a slope of 1/3. What can she classify ABCD as?

a)

A rectangle

b)

A square

c)

A rhombus

d)

Just a parallelogram

105.

Use the distance formula to see if side AB is congruent to side BC.

a)

Yes they are congruent

b)

No, they are not congruent

106.

Use the distance formula to see if side BC is congruent to side AD.

a)

Yes they are congruent

b)

No, they are not congruent

107.

What is the most specific name for quadrilateral ARMY?

a)

Paralellogram

b)

Square

c)

Rectangle

d)

Rhombus

108.

What is the most specific name for quadrilateral DOGS?

a)

Rhombus

b)

Rectangle

c)

Parallelogram

d)

Square

109.

What is the most specific name for quadrilateral FISH?

a)

Parallelogram

b)

Square

c)

Rectangle

d)

Rhombus

110.

[END (Coordinate) Quadrilateral Proofs] What is the most specific name for quadrilateral NOSE?

a)

Square

b)

Parallelogram

c)

Rectangle

d)

Rhombus

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